Dense Star Clusters Research Articles

A new hybrid technique for modeling dense star clusters

The “gravitational million-body problem,” to model the dynamical evolution of a self-gravitating, collisional N-body system with ∼106 particles over many relaxation times, remains a major challenge in computational astrophysics. Unfortunately, current techniques to model such systems suffer from severe limitations. A direct N-body simulation with more than 105 particles can require months or even years to complete, while an orbit-sampling Monte Carlo approach cannot adequately model the dynamics in a dense cluster core, particularly in the presence of many black holes. We have developed a new technique combining the precision of a direct N-body integration with the speed of a Monte Carlo approach. Our Rapid And Precisely Integrated Dynamics code, the RAPID code, statistically models interactions between neighboring stars and stellar binaries while integrating directly the orbits of stars or black holes in the cluster core. This allows us to accurately simulate the dynamics of the black holes in a realistic globular cluster environment without the burdensome N^{2} scaling of a full N-body integration. We compare RAPID models of idealized globular clusters to identical models from the direct N-body and Monte Carlo methods. Our tests show that RAPID can reproduce the half-mass radii, core radii, black hole ejection rates, and binary properties of the direct N-body models far more accurately than a standard Monte Carlo integration while remaining significantly faster than a full N-body integration. With this technique, it will be possible to create more realistic models of Milky Way globular clusters with sufficient rapidity to explore the full parameter space of dense stellar clusters.

Detecting stellar lensing of gravitational waves with ground-based observatories

We investigate the ability of ground based gravitational wave observatories to detect gravitational wave lensing events caused by stellar mass lenses. We show that LIGO and Virgo possess the sensitivities required to detect lenses with masses as small as $\sim 30 M_\odot$ provided that the gravitational wave is observed with a signal-to-noise ratio of $\sim30$. Third generation observatories will allow detection of gravitational wave lenses with masses of $\sim 1 M_\odot$. Finally, we discuss the possibility of lensing by multiple stars, as is the case if the gravitational radiation is passing through galactic nucleus or a dense star cluster.

Redshift Evolution of the Black Hole Merger Rate from Globular Clusters

Abstract As the sensitivity of current and future gravitational-wave detectors improves, it will become possible to measure the evolution of the binary black hole merger rate with redshift. Here, we combine detailed fits to state-of-the-art dynamical models of binary black hole formation in dense star clusters with a cosmological model of cluster formation across cosmic time. We find a typical merger rate of 14 Gpc−3 yr−1 in the local universe, with a reasonable range of 4–18 Gpc−3 yr−1, depending on the rate of cluster disruption and the cluster initial mass function. This rate increases by a factor of 6 to redshift z = 2.7 before declining at higher redshifts. We compare the merger rate from binaries produced in clusters to similar estimates from isolated binaries and triples in galactic fields, and discuss various ways that these different formation channels could add up to the current merger rate observed by the Laser Interferometer Gravitational-Wave Observatory/Virgo.

Gamma-ray and X-ray emission from the Galactic centre: hints on the nuclear star cluster formation history

The Milky Way centre exhibits an intense flux in the gamma and X-ray bands, whose origin is partly ascribed to the possible presence of a large population of millisecond pulsars (MSPs) and cataclysmic variables (CVs), respectively. However, the number of sources required to generate such an excess is much larger than what is expected from in situ star formation and evolution, opening a series of questions about the formation history of the Galactic nucleus. In this paper we make use of direct $N$-body simulations to investigate whether these sources could have been brought to the Galactic centre by a population of star clusters that underwent orbital decay and formed the Galactic nuclear star cluster (NSC). Our results suggest that the gamma ray emission is compatible with a population of MSPs that were mass segregated in their parent clusters, while the X-ray emission is consistent with a population of CVs born via dynamical interactions in dense star clusters. Combining observations with our modelling, we explore how the observed $\gamma$ ray flux can be related to different NSC formation scenarios. Finally, we show that the high-energy emission coming from the galactic central regions can be used to detect black holes heavier than $10^5\Ms$ in nearby dwarf galaxies.

Mapping the core of the Tarantula Nebula with VLT-MUSE

We introduce VLT-MUSE observations of the central 2′× 2′ (30 × 30 pc) of the Tarantula Nebula in the Large Magellanic Cloud. The observations provide an unprecedented spectroscopic census of the massive stars and ionised gas in the vicinity of R136, the young, dense star cluster located in NGC 2070, at the heart of the richest star-forming region in the Local Group. Spectrophotometry and radial-velocity estimates of the nebular gas (superimposed on the stellar spectra) are provided for 2255 point sources extracted from the MUSE datacubes, and we present estimates of stellar radial velocities for 270 early-type stars (finding an average systemic velocity of 271 ± 41 km s−1). We present an extinction map constructed from the nebular Balmer lines, with electron densities and temperatures estimated from intensity ratios of the [S II], [N II], and [S III] lines. The interstellar medium, as traced by Hα and [N II] λ6583, provides new insights in regions where stars are probably forming. The gas kinematics are complex, but with a clear bi-modal, blue- and red-shifted distribution compared to the systemic velocity of the gas centred on R136. Interesting point-like sources are also seen in the eastern cavity, western shell, and around R136; these might be related to phenomena such as runaway stars, jets, formation of new stars, or the interaction of the gas with the population of Wolf–Rayet stars. Closer inspection of the core reveals red-shifted material surrounding the strongest X-ray sources, although we are unable to investigate the kinematics in detail as the stars are spatially unresolved in the MUSE data. Further papers in this series will discuss the detailed stellar content of NGC 2070 and its integrated stellar and nebular properties.

Post-Newtonian Dynamics in Dense Star Clusters: Highly Eccentric, Highly Spinning, and Repeated Binary Black Hole Mergers.

We present models of realistic globular clusters with post-Newtonian dynamics for black holes. By modeling the relativistic accelerations and gravitational-wave emission in isolated binaries and during three- and four-body encounters, we find that nearly half of all binary black hole mergers occur inside the cluster, with about 10% of those mergers entering the LIGO/Virgo band with eccentricities greater than 0.1. In-cluster mergers lead to the birth of a second generation of black holes with larger masses and high spins, which, depending on the black hole natal spins, can sometimes be retained in the cluster and merge again. As a result, globular clusters can produce merging binaries with detectable spins regardless of the birth spins of black holes formed from massive stars. These second-generation black holes would also populate any upper mass gap created by pair-instability supernovae.

Dynamical tides in highly eccentric binaries: chaos, dissipation, and quasi-steady state

Highly eccentric binary systems appear in many astrophysical contexts, ranging from tidal capture in dense star clusters, precursors of stellar disruption by massive black holes, to high-eccentricity migration of giant planets. In a highly eccentric binary, the tidal potential of one body can excite oscillatory modes in the other during a pericenter passage, resulting in energy exchange between the modes and the binary orbit. These modes exhibit one of three behaviors over multiple passages: low-amplitude oscillations, large amplitude oscillations corresponding to a resonance between the orbital frequency and the mode frequency, and chaotic growth. We study these phenomena with an iterative map, fully exploring how the mode evolution depends on the pericenter distance and other parameters. In addition, we show that the dissipation of mode energy results in a quasi-steady state, with gradual orbital decay punctuated by resonances, even in systems where the mode amplitude would initially grow stochastically. A newly captured star around a black hole can experience significant orbital decay and heating due to the chaotic growth of the mode amplitude and dissipation. A giant planet pushed into a high-eccentricity orbit may experience a similar effect and become a hot or warm Jupiter.

The kinematics of the Scorpius-Centaurus OB association from Gaia DR1

We present a kinematic study of the Scorpius-Centaurus (Sco-Cen) OB association (Sco OB2) using Gaia DR1 parallaxes and proper motions. Our goal is to test the classical theory that OB associations are the expanded remnants of dense and compact star clusters disrupted by processes such as residual gas expulsion. Gaia astrometry is available for 258 out of 433 members of the association, with revised Hipparcos astrometry used for the remainder. We use these data to confirm that the three subgroups of Sco-Cen are gravitationally unbound and have non-isotropic velocity dispersions, suggesting that they have not had time to dynamically relax. We also explore the internal kinematics of the subgroups to search for evidence of expansion. We test Blaauw's classical linear model of expansion, search for velocity trends along the Galactic axes, compare the expanding and non-expanding convergence points, perform traceback analysis assuming both linear trajectories and using an epicycle approximation, and assess the evidence for expansion in proper motions corrected for virtual expansion/contraction. None of these methods provide coherent evidence for expansion of the subgroups, with no evidence to suggest that the subgroups had a more compact configuration in the past. We find evidence for kinematic substructure within the subgroups that supports the view that they were not formed by the disruption of individual star clusters. We conclude that Sco-Cen was likely to have been born highly substructured, with multiple small-scale star formation events contributing to the overall OB association, and not as single, monolithic burst of clustered star formation.

The detection rates of merging binary black holes originating from star clusters and their mass function

Abstract Advanced LIGO (Laser Interferometer Gravitational Wave Observatory) observations achieved the first detection of the gravitational wave, which was from a merging binary black hole (BBH). In the near future, more merger events will be observed, and the mass distribution of them will become available. The mass distribution of merger events reflects the evolutionary path of BBHs: dynamical formation in dense star clusters or common envelope evolution from primordial binaries. In this paper, we estimate the detection rate of merging BBHs which dynamically formed in dense star clusters by combining the results of N-body simulations, modeling of globular clusters, and cosmic star-cluster formation history. We estimate that the merger rate density in the local universe within the redshift of 0.1 is 13–57 Gpc−3 yr−1. We find that the detection rate is 0.23–4.6 per year for the current sensitivity limit and that it would increase to 5.1–99 per year for the designed sensitivity which will be achieved in 2019. The distribution of merger rate density in the local universe as a function of redshifted chirp mass has a peak close to the low-mass end. The chirp mass function of the detected mergers, on the other hand, has a peak at the high-mass end, but is almost flat. This difference is simply because the detection range is larger for more massive BBHs.

Probing stellar binary black hole formation in galactic nuclei via the imprint of their center of mass acceleration on their gravitational wave signal

Multi-frequency gravitational wave (GW) observations are useful probes of the formation processes of coalescing stellar-mass binary black holes (BBHs). We discuss the phase drift in the GW inspiral waveform of the merging BBH caused by its center-of-mass acceleration. The acceleration strongly depends on the location where a BBH forms within a galaxy, allowing observations of the early inspiral phase of LIGO-like BBH mergers by the Laser Interferometer Space Antenna (LISA) to test the formation mechanism. In particular, BBHs formed in dense nuclear star clusters or via compact accretion disks around a nuclear supermassive black hole in active galactic nuclei would suffer strong acceleration, and produce large phase drifts measurable by LISA. The host galaxies of the coalescing BBHs in these scenarios can also be uniquely identified in the LISA error volume, without electromagnetic counterparts. A non-detection of phase drifts would rule out or constrain the contribution of the nuclear formation channels to the stellar-mass BBH population.

Formation of intermediate-mass black holes through runaway collisions in the first star clusters

We study the formation of massive black holes in the first star clusters. We first locate star-forming gas clouds in proto-galactic haloes of $\gtrsim \!10^7\,{\rm M}_{\odot}$ in cosmological hydrodynamics simulations and use them to generate the initial conditions for star clusters with masses of $\sim \!10^5\,{\rm M}_{\odot}$. We then perform a series of direct-tree hybrid $N$-body simulations to follow runaway stellar collisions in the dense star clusters. In all the cluster models except one, runaway collisions occur within a few million years, and the mass of the central, most massive star reaches $\sim \!400-1900\,{\rm M}_{\odot}$. Such very massive stars collapse to leave intermediate-mass black holes (IMBHs). The diversity of the final masses may be attributed to the differences in a few basic properties of the host haloes such as mass, central gas velocity dispersion, and mean gas density of the central core. Finally, we derive the IMBH mass to cluster mass ratios, and compare them with the observed black hole to bulge mass ratios in the present-day Universe.

Binary Black Hole Mergers from Field Triples: Properties, Rates, and the Impact of Stellar Evolution

Abstract We consider the formation of binary black hole (BH) mergers through the evolution of field massive triple stars. In this scenario, favorable conditions for the inspiral of a BH binary are initiated by its gravitational interaction with a distant companion, rather than by a common-envelope phase invoked in standard binary evolution models. We use a code that follows self-consistently the evolution of massive triple stars, combining the secular triple dynamics (Lidov–Kozai cycles) with stellar evolution. After a BH triple is formed, its dynamical evolution is computed using either the orbit-averaged equations of motion, or a high-precision direct integrator for triples with weaker hierarchies for which the secular perturbation theory breaks down. Most BH mergers in our models are produced in the latter non-secular dynamical regime. We derive the properties of the merging binaries and compute a BH merger rate in the range (0.3–1.3) Gpc−3 yr−1, or up to ≈2.5 Gpc−3 yr−1 if the BH orbital planes have initially random orientation. Finally, we show that BH mergers from the triple channel have significantly higher eccentricities than those formed through the evolution of massive binaries or in dense star clusters. Measured eccentricities could therefore be used to uniquely identify binary mergers formed through the evolution of triple stars. While our results suggest up to ≈10 detections per year with Advanced-LIGO, the high eccentricities could render the merging binaries harder to detect with planned space based interferometers such as LISA.

Blossoms from black hole seeds: properties and early growth regulated by supernova feedback

Massive black holes (BHs) inhabit local galaxies, including the Milky Way and some dwarf galaxies. BH formation, occurring at early cosmic times, must account for the properties of BHs in today's galaxies, notably why some galaxies host a BH, and others do not. We investigate the formation, distribution and growth of BH `seeds' by using the adaptive mesh refinement code Ramses. We develop an implementation of BH formation in dense, low-metallicity environments, as advocated by models invoking the collapse of the first generation of stars, or of dense nuclear star clusters. The seed masses are computed one-by-one on-the-fly, based on the star formation rate and the stellar initial mass function. This self-consistent method to seed BHs allows us to study the distribution of BHs in a cosmological context and their evolution over cosmic time. We find that all high-mass galaxies tend to a host a BH, whereas low-mass counterparts have a lower probability of hosting a BH. After the end of the epoch of BH formation, this probability is modulated by the growth of the galaxy. The simulated BHs connect to low-redshift observational samples, and span a similar range in accretion properties as Lyman-Break Analogs. The growth of BHs in low-mass galaxies is stunted by strong supernova feedback. The properties of BHs in dwarf galaxies thus remain a testbed for BH formation. Simulations with strong supernova feedback, which is able to quench BH accretion in shallow potential wells, produce galaxies and BHs in better agreement with observational constraints.

Galactic Dark Matter Halos and Globular Cluster Populations. III. Extension to Extreme Environments

Abstract The total mass in the globular cluster (GC) system of a galaxy is empirically a near-constant fraction of the total mass of the galaxy across a range of 105 in galaxy mass. This trend is radically unlike the strongly nonlinear behavior of total stellar mass M ⋆ versus M h . We discuss extensions of this trend to two more extreme situations: (a) entire clusters of galaxies and (b) the ultra-diffuse galaxies (UDGs) recently discovered in Coma and elsewhere. Our calibration of the ratio from normal galaxies, accounting for new revisions in the adopted mass-to-light ratio for GCs, now gives as the mean absolute mass fraction. We find that the same ratio appears valid for galaxy clusters and UDGs. Estimates of in the four clusters we examine tend to be slightly higher than for individual galaxies, but more data and better constraints on the mean GC mass in such systems are needed to determine if this difference is significant. We use the constancy of to estimate total masses for several individual cases; for example, the total mass of the Milky Way is calculated to be . Physical explanations for the uniformity of are still descriptive, but point to a picture in which massive dense star clusters in their formation stages were relatively immune to the feedback that more strongly influenced lower-density regions where most stars form.

ILLUMINATING BLACK HOLE BINARY FORMATION CHANNELS WITH SPINS IN ADVANCED LIGO

ABSTRACT The recent detections of the binary black hole mergers GW150914 and GW151226 have inaugurated the field of gravitational-wave astronomy. For the two main formation channels that have been proposed for these sources, isolated binary evolution in galactic fields and dynamical formation in dense star clusters, the predicted masses and merger rates overlap significantly, complicating any astrophysical claims that rely on measured masses alone. Here, we examine the distribution of spin–orbit misalignments expected for binaries from the field and from dense star clusters. Under standard assumptions for black hole natal kicks, we find that black hole binaries similar to GW150914 could be formed with significant spin–orbit misalignment only through dynamical processes. In particular, these heavy-black hole binaries can only form with a significant spin–orbit anti-alignment in the dynamical channel. Our results suggest that future detections of merging black hole binaries with measurable spins will allow us to identify the main formation channel for these systems.

Multiphase environment of compact galactic nuclei: the role of the nuclear star cluster

We study the conditions for the onset of Thermal Instability in the innermost regions of compact galactic nuclei, where the properties of the interstellar environment are governed by the interplay of quasi-spherical accretion onto a supermassive black hole (SMBH) and the heating/cooling processes of gas in a dense nuclear star cluster. Stellar winds are the source of material for radiatively inefficient (quasi-spherical, non-magnetised) inflow/outflow onto the central SMBH, where a stagnation point develops within the Bondi type accretion. We study the local thermal equilibrium to determine the parameter space which allows cold and hot phases in mutual contact to co-exist. We include the effects of mechanical heating by stellar winds and radiative cooling/heating by the ambient field of the dense star cluster. We consider two examples: the Nuclear Star Cluster (NSC) in the Milky Way central region (including the gaseous Mini-spiral of Sgr~A*), and the Ultra-Compact Dwarf galaxy M60-UCD1. We find that the two systems behave in different ways because they are placed in different areas of parameter space in the instability diagram: gas temperature vs. dynamical ionization parameter. In the case of Sgr~A*, stellar heating prevents the spontaneous formation of cold clouds. The plasma from stellar winds joins the hot X-ray emitting phase and forms an outflow. In M60-UCD1 our model predicts spontaneous formation of cold clouds in the inner part of the galaxy. These cold clouds may survive since the cooling timescale is shorter than the inflow/outflow timescale.

ELISA eccentricity measurements as tracers of binary black hole formation

Up to hundreds of black hole binaries individually resolvable by eLISA will coalesce in the Advanced LIGO/Virgo band within ten years, allowing for multi-band gravitational wave observations. Binaries formed via dynamical interactions in dense star clusters are expected to have eccentricities $e_0\sim 10^{-3}$-$10^{-1}$ at the frequencies $f_0=10^{-2}$ Hz where eLISA is most sensitive, while binaries formed in the field should have negligible eccentricity in both frequency bands. We estimate that eLISA should always be able to detect a nonzero $e_0$ whenever $e_0\gtrsim 10^{-2}$; if $e_0\sim 10^{-3}$, eLISA should detect nonzero eccentricity for a fraction $\sim 90\%$ ($\sim 25\%$) of binaries when the observation time is $T_{\rm obs}=5$ ($2$) years, respectively. Therefore eLISA observations of BH binaries have the potential to distinguish between field and cluster formation scenarios.

The chaotic four-body problem in Newtonian gravity– I. Identical point-particles

In this paper, we study the chaotic four-body problem in Newtonian gravity. Assuming point particles and total encounter energies $\le$ 0, the problem has three possible outcomes. We describe each outcome as a series of discrete transformations in energy space, using the diagrams first presented in Leigh \& Geller (2012; see the Appendix). Furthermore, we develop a formalism for calculating probabilities for these outcomes to occur, expressed using the density of escape configurations per unit energy, and based on the Monaghan description originally developed for the three-body problem. We compare this analytic formalism to results from a series of binary-binary encounters with identical point particles, simulated using the \texttt{FEWBODY} code. Each of our three encounter outcomes produces a unique velocity distribution for the escaping star(s). Thus, these distributions can potentially be used to constrain the origins of dynamically-formed populations, via a direct comparison between the predicted and observed velocity distributions. Finally, we show that, for encounters that form stable triples, the simulated single star escape velocity distributions are the same as for the three-body problem. This is also the case for the other two encounter outcomes, but only at low virial ratios. This suggests that single and binary stars processed via single-binary and binary-binary encounters in dense star clusters should have a unique velocity distribution relative to the underlying Maxwellian distribution (provided the relaxation time is sufficiently long), which can be calculated analytically.

Hierarchical black hole triples in young star clusters: impact of Kozai–Lidov resonance on mergers

Mergers of compact object binaries are one of the most powerful sources of gravitational waves (GWs) in the frequency range of second-generation ground-based gravitational wave detectors (Advanced LIGO and Virgo). Dynamical simulations of young dense star clusters (SCs) indicate that ~27 per cent of all double compact object binaries are members of hierarchical triple systems (HTs). In this paper, we consider 570 HTs composed of three compact objects (black holes or neutron stars) that formed dynamically in N-body simulations of young dense SCs. We simulate them for a Hubble time with a new code based on the Mikkola's algorithmic regularization scheme, including the 2.5 post-Newtonian term. We find that ~88 per cent of the simulated systems develop Kozai-Lidov (KL) oscillations. KL resonance triggers the merger of the inner binary in three systems (corresponding to 0.5 per cent of the simulated HTs), by increasing the eccentricity of the inner binary. Accounting for KL oscillations leads to an increase of the total expected merger rate by ~50 per cent. All binaries that merge because of KL oscillations were formed by dynamical exchanges (i.e. none is a primordial binary) and have chirp mass >20 Msun. This result might be crucial to interpret the formation channel of the first recently detected GW events.

Molecular gas kinematics of the CMZ: Great oaks from little acorns grow

AbstractThe central molecular zone (CMZ) hosts some of the most massive and dense molecular clouds and star clusters in the Galaxy, offering an important window into star formation under extreme conditions. Star formation in this extreme environment may be closely linked to the 3-D distribution and orbital dynamics of the gas. Here I discuss how our new, accurate description of the {l,b,v} structure of the CMZ is helping to constrain its 3-D geometry. I also present the discovery of a highly-regular, corrugated velocity field located just upstream from the dust ridge molecular clouds (which include G0.253+0.016 and Sgr B2). The extremes in this velocity field correlate with a series of massive (~ 104 M⊙) cloud condensations. The corrugation wavelength (~23 pc) and cloud separation (~8 pc) closely agree with the predicted Toomre (~17 pc) and Jeans (~6 pc) lengths, respectively. I conclude that gravitational instabilities are driving the formation of molecular clouds within the Galactic Centre gas stream. Furthermore, I suggest that these seeds are the historical analogues of the dust ridge molecular clouds – possible progenitors of some of the most massive and dense molecular clouds in the Galaxy. If our current best understanding for the 3-D geometry of this system is confirmed, these clouds may pinpoint the beginning of an evolutionary sequence that can be followed, in time, from cloud condensation to star formation.